The quality of the reduced-order zonotope is measured by the ratio between its volume and that of the original zonotope before reduction, defined in Fig. REF  (lower). We are able to run this evaluation for lower-dimensional cases because computing the exact volume of a zonotope is difficult for high-dimensional case due to the combinatorial complexity [1]}. In Fig. REF  (lower), the volume ratio increases with the the original zonotope's order because higher order means more freedom in selecting the generators to combine.
In the presented cases, the ratio is close to one if the original zonotope's order is greater than three.
